Effect of different jump distributions on the dynamics of jump processes
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The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.
Published Version (Please cite this version)10.1103/PhysRevE.81.061133
Publication InfoDaly, Edoardo; & Porporato, Amilcare (2010). Effect of different jump distributions on the dynamics of jump processes. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 81(6). pp. 61133. 10.1103/PhysRevE.81.061133. Retrieved from https://hdl.handle.net/10161/4288.
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Adjunct Professor in the Department of Civil and Environmental Engineering
Amilcare Porporato earned a Master Degree in Civil Engineering (summa cum laude) in 1992 and his Ph.D. in 1996 from Polytechnic of Turin. He was appointed Assistant Professor in the Department of Hydraulics of the Polytechnic of Turin, and he moved to Duke University in 2003, where he is now Full Professor in the Department of Civil and Environmental Engineering with a secondary appointment with the Nicholas School of the Environment. In June 1996, Porporato received the Arturo Parisatti